Problems Open and Otherwise

# Topological dynamics

## Periodic points

- Describe the set of periodic points or points with periodic itineraries in various settings (non-zero topological entropy, piecewise isometries,…)
- Count them (find a nice zeta function)

## Symbolic dynamics

- describe its structure (e.g., by defining an abstract class to which the considered symbolic dynamics belong and which implies the considered properties)
- relate it precisely to the PA dynamics (e.g., in which case does it have the same topological entropy?)

## Entropy

- dependence on the PA dynamics
- computation from geometric and combinatorial data

# Ergodic theory

## SRB measures

- Simplify Tsujii's general construction
- Find something like it for the piecewise hyperbolic situation, maybe using Baladi-Gouëzel recent work (prove first a generic result?)
- Prove Palis conjecture on SRB measures for PA dynamics, for instance for the Lozi family

## Maximal entropy measures

- Find in which settings:
- they always exist (e.g., homeomorphisms in higher dimension?)
- they form a finite-dimensional simplex

page revision: 1, last edited: 10 Mar 2009 16:40